The origin of UHECR can be modelled essentially in two ways: (i) assuming the presence of different classes of sources: one injecting heavy nuclei with hard spectrum and the other only proton and helium nuclei with soft spectrum [1]}, [2]} or (ii) identifying a peculiar class of sources that could provide at the same time a steep light component and a flat heavy one [3]}, [4]}, [5]}. The second approach is based on a specific hypothesis on the sources that should be surrounded by an intense radiation field that, through photo-disintegration of heavy nuclei in the source neighbourhood, can provide a light component of (secondary) protons with a steep spectrum together with a hard and heavier component [3]}, [4]}. It should be also noted that the diffusive shock acceleration mechanism produces steep injections of particles with \(\gamma _g > 2\) , while acceleration due to potential drops typically imply \(\gamma _g\simeq 1\)  (see [8]}, [9]} and references therein).
